Construction of Efficient Mixed-Level Fractional Factorial Designs

Mixed-level factorial experimental designs involve factors with different numbers of levels. Full factorial designs require runs at all possible combinations of the factor levels. As the number of factors and/or factor levels increases, the total number of experiments increases dramatically. As a result, interest has focused on developing orthogonal or near-orthogonal mixed-level fractional factorial designs. Currently existing mixed-level designs are all balanced. However, relaxing the requirement of balance may result in a reduced number of experimental runs in practice. The objective of this paper is to develop mixed-level fractional factorial designs with economical run sizes that are as nearly balanced and orthogonal as possible. A new criterion is developed to assess the degree of near-balance for comparing and constructing designs. A modified J2-optimality criterion is used for evaluating design near orthogonality. These criteria are combined and used to assess different design alternatives. Three algorithms are then compared and used to build designs with desirable combinations of near balance and near orthogonality.